I honestly think I could get away with one bike and three sets of wheels. Seriously! Think about it:
Take a bike like my Univega (or a Surly CC, or some such light touring/CX bike). Get one set of rims that wears slick 38c tires. These would be the commuter/mountain bike tires. Another set would be with 27-ish-c tires for the quick rides and brevets. The final set would be with 38ish knobbies for fun in the mud.
It's comfy, it can be a mountain/road/commuter/light touring bike, and it doesn't look horrific.
That said, you can never have too many bikes. I just picked up my 10th last night. I should state though that, including this one (which still needs to be built up), 6 of them are riders, two are awaiting funds to be rebuilt, and two are parts.